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Zbl 1234.60084
Lefebvre, Mario
Maximizing the mean exit time of a Brownian motion from an interval. (English)
[J] Int. J. Stoch. Anal. 2011, Article ID 296259, 5 p. (2011). ISSN 2090-3332; ISSN 2090-3340/e

Summary: Let $X(t)$ be a controlled one-dimensional standard Brownian motion starting from $x\in(-d,d)$. The problem of optimally controlling $X(t)$ until $|X(t)|=d$ for the first time is solved explicitly in a particular case. The maximal value that the instantaneous reward given for survival in $(-d,d)$ can take is determined.

MSC 2000:: *60J65 Brownian motion
93E20 Optimal stochastic control (systems)

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Zentralblatt MATH Berlin [Germany]